A simple pendulum is released from rest with the string in horizontal position. The vertical component of the velocity of the bob becomes maximum, when the string makes an angle `theta` with the vertical. The angle `theta` is equal to

Options

A. `(pi)/(4)`
B. `cos^(-1)((1)/(sqrt(3)))`
C. `sin^(-1)((1)/(sqrt(3)))`
D. `(pi)/(3)`

Answer

B

Explanation

`h=Rcostheta`
`v_(0)=sqrt(2gh)=sqrt(2gRcostheta)`

Vertical componet of velocity is,
`v=v_(0)sintheta`
`=sinthetasqrt(2gRcostheta)`
For `v` to be maximum
`(dv)/(dtheta)=0`
:. `[costhetasqrt(2gRcostheta)]`